Definitely lose the car first thing. Drop it off at the airport and take the bus, either Dublin Bus (more of stops, not always good luggage storage space), or Aircoach (more expensive, but worth it because it has less stops and you stow your luggage in the under bus storage compartment). Buy your ticket at the Dublin Tourism counter at the airport (you might be able to buy one at the bus, but sometimes it gets full fast). You can get info on mini-bus day trips to the Boyne Valley there, and you might be able to book one as well.
AirCoach will take you to the City Centre - one of the stops is in front of Trinity College. I think you can catch a Dublin Bus from there if you need to get closer to your hotel/hostel (or stay at the College, if it's summer).
When you get situated in Dublin, you can also go to the Tourism Office (near the college) to book a day trip to the Boyne Valley.
For a couple of days in Dublin city, try a Musical Pub Crawl or a Literary Pub Crawl one evening - they're fun, informative, and they get you into crowded, popular pubs when you might not otherwise be able to find a seat. During the day, try the 1916 Rebellion Walking Tour; A Historical Walking Tour; A tour of Trinity College, or just see the Book of Kells (if the line isn't a mile long); Walk down Grafton Street to get to St. Stephen's Green for a stroll through the park; If you don't go on the 1916 tour, at least try to get to the General Post Office and/or Kilmainham Gaol (Jail).
Skip the Guinness Storehouse tour (too Hollywood/Disneyfied/commercialized/noisy for me), unless you pay admission for a tour but just take the elevator to the bar at the top for a free pint and a 360 view of the city. (Worth it if you have the time.)
There's so much more... Try http://www.hidden-dublin.com